Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem C. 1305. (September 2015)

C. 1305. A spiral is made out of a square of side \(\displaystyle n\) units, as shown in the figure, by always breaking the line 1 unit before reaching the already existing part of the spiral. Similarly, a spiral is made out of a regular triangle of side \(\displaystyle 1.8n\) units by breaking the line 1.8 units before closing up. (The diagram shows the two spirals for the case of \(\displaystyle n = 4\).) For what value of n will the lengths of the two spirals be equal?

(5 pont)

Deadline expired on October 12, 2015.


250 students sent a solution.
5 points:102 students.
4 points:61 students.
3 points:10 students.
2 points:9 students.
1 point:5 students.
0 point:58 students.
Unfair, not evaluated:5 solutionss.

Problems in Mathematics of KöMaL, September 2015